Tree Physiology 21, 261–266
© 2001 Heron Publishing—Victoria, Canada
Growth stress distribution in leaning trunks of Cryptomeria japonica
YAN S. HUANG,1 SHIN S. CHEN,1 TSAN P. LIN2 and YUH S. CHEN1
1
Division of Forest Utilization, Taiwan Forestry Research Institute, 53 Nan-Hai Road, Taipei 100, Taiwan
2
Division of Silviculture, Taiwan Forestry Research Institute, 53 Nan-Hai Road, Taipei 100, Taiwan
Received March 10, 2000
Summary The distribution of growth stresses in leaning
trunks of Cryptomeria japonica (L.f.) D. Don was determined
by measuring the stresses released by the kerf method with
strain gauges glued at specified positions along the trunks. Effects of both tree height and peripheral positions on the surface
of leaning trunks on surface growth stress were determined.
The inner residual growth strains in leaning trunks were also
measured. We found high compression stresses in the lower
side of leaning trunks that differed greatly from the tensile
stresses in normal erect trunks. However, transverse compression stress was found around the tree trunk in both normal and
compression wood. In leaning trees, the distribution of internal
stresses in the bent trunk portion differed from that in the erect
trunk portion, being compressive on the outside and tensile on
the inside. The resistant moment introduced by compression
stress generated in compression wood is released by the bending of the leaning trunk. The bending stresses are then superimposed on the original internal growth stress. We demonstrated
that Poisson’s effect of longitudinal stresses should be considered when evaluating transverse surface growth stresses. The
existence and intensity of compression wood development can
be assessed by growth stress measurements. We conclude that
the compressing force of compression wood functions physiologically to give an upward righting response in a leaning
trunk.
Keywords: compression wood, residual internal stress, surface growth strain, strain gauge.
Introduction
Tree trunks accumulate growth stresses during each year of
growth that are similar to the residual stresses that occur in artificial material during processing. These growth stresses represent an important physiological mechanism enabling the
tree to adjust to environmental conditions. In a normal, erectgrowing trunk, newly formed xylem cells from the vascular
cambium become lignified and generate tension stress in the
longitudinal direction and compression stress in the tangential
direction. This combination of stresses around the vascular
cambium occurs each year, resulting in a regular distribution
of stresses in the diametral plane. As a result, tension stress is
formed in the outer part and compression stress in the inner
part of a trunk. These stresses are a key factor in helping tree
trunks resist wind strikes and in preventing frost from cracking
the xylem during severe winters (Matheck and Kubler 1995).
Upward curving is a common tree growth phenomenon. Conifers usually form compression wood on the lower side of
branches or leaning trunks (Panshin et al. 1964, Timell
1986a). The stress generated from this specialized tissue differs from that of normal wood. Compression wood produces
compression stress in a longitudinal direction that constrains
extension of the wood. In contrast, in most angiosperm trees,
tension wood forms as a specialized tissue on the upper side of
branches and leaning trunks. Tension wood also generates
greater tensile stress than normal wood, constraining shrinkage in the longitudinal direction. Compression wood and tension wood force the leaning trunks of coniferous and broadleaf
tree species, respectively, to grow upward.
Although growth stresses have important physiological
functions in maintaining the distribution of stress in equilibrium in living trunks, growth stresses released during felling
and sawing may cause splitting of the center, curving of sawn
timber, and other difficulties. From the viewpoint of wood utilization, a detailed knowledge of the development of growth
stress is needed to identify possible methods that could be used
to ease or release these stresses during processing (Okuyama
and Sasaki 1979, Archer 1986, Timell 1986b, Okuyama et al.
1988). Because compression wood has a different cell structure, chemical composition, and growth stress than normal
wood, it provides a suitable material for studying the mechanism of growth stress.
Several possible mechanisms of growth stress have been investigated. Boyd (1972) proposed the “lignin-swelling hypothesis,” based on the observed swelling of the thickness of
cell walls during lignification, to explain the mechanism of incidence of longitudinal, tangential and radial growth stresses.
Yamamoto et al. (1991) studied the influence on growth stress
of microfibril angle of the S2 layer in the cell wall and the
lignin content of tracheids in Chamaecyparis obtusa (Siebold
& Zucc.) Endl. Archer (1987) investigated the mechanism for
growth stress generation that involves a contractive strain in
the microfibril direction and an expansive strain in the transverse direction in the developing walls of wood cells. He concluded that the tensile stress in normal wood becomes a
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HUANG, CHEN, LIN AND CHEN
compression stress in compression wood as the microfibril angle increases.
Previously, we reported the distribution of growth stresses
in normal wood of Cryptomeria japonica (L.f.) D. Don
(Huang et al. 1998). Here, we present the distribution of
growth stress and strain in compression wood of leaning
trunks of C. japonica.
Materials and methods
Six leaning 25- to 35-year-old, plantation-grown trees of
Cryptomeria japonica at Chilanshan Station (121°15′–
121°30′ E, 24°15′–24°45′ N, altitude 1100 m), Forest Conservation Institute, Taiwan, were used to measure surface growth
stress and residual internal stress (Figure 1). Trees A, B and C
were used to measure peripheral surface growth strain in living trees, Tree E was used to determine the effect of tree height
on surface growth stress and strain, and Trees D and F were
used to measure residual internal growth strain in leaning
trunks. The circumferences below breast height of standing
trees A, B and C were measured. For each standing tree, the
entire trunk length was divided into six equal parts, with the
upper side of the leaning trunk designated as 0° and the lower
side as 180°. After removing the bark at specified positions,
electrical resistance strain gauges were attached to the xylem
in both longitudinal and transverse directions, with
cyanoacrylate adhesive. A portable digital strain meter (Model
UCAM-1A Kyowa Ltd., Tokyo, Japan) with a 40-channel
scanner (USB-11A) was used for measurement. After calibrating the strain gauges to zero, the surface growth strain was released by the kerf method (Sasaki et al. 1978), i.e., grooves
1–1.5 cm deep were made in the xylem around the strain gauge
with a handsaw and chain saw and the released strain was determined immediately. Trees A, B and C were measured at
heights of 110, 80 and 40 cm above ground level, respectively,
and their mean diameters at these heights were 50, 32 and 34
cm, respectively. The other three leaning trees, D, E and F,
Figure 1. Leaning trunks of Trees A–F.
which were felled, had mean diameters of 30, 24 and 26 cm,
respectively, at 1-m height. For tree E (see Figure 4), the felled
trunk was sawn transversely every 1–1.5 m, and longitudinal
surface strains were measured by the kerf method at the middle point of each segment to determine the influence of tree
height on growth stresses. In addition, disks of wood about 20
cm thick were taken at the measuring position of each segment. Specimens of 1 cm (width) × 1 cm (length) × 18 cm
(thick) were sampled from the disk and used in a static bending test to determine the modulus of elasticity. The modulus of
elasticity was used to calculate growth stresses. For Trees D
and F, diametral planks, 30 cm long and 2 cm thick, located in
the center of the curving trunk, were obtained by chain saw
and hand plane (Figure 2). At the center of the curving trunk,
about 0.8 m above ground, elliptical cross-sections were
found with lengths of the long axis (i.e., the width of the diametral plank) and short axis being 36 and 24 cm, respectively,
for Tree D, and 28.5 and 23 cm, respectively, for Tree F. Strain
gauges were glued at the center of the length of each diametral
plank at intervals of 1.5 cm radially, in the longitudinal direction (see Figure 2). Longitudinal residual strains on the diametral planks were then measured by cross-cutting each plank
with a handsaw at 1 cm above the strain gauges and then ripping among the gauges, so that the residual strain could be
Figure 2. Measurement of released strain inside the leaning trunk of
Tree D.
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GROWTH STRESS IN LEANING TRUNKS
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measured.
Calculation of growth stress
A tree trunk can be assumed to be an orthotropic body, and
surface stresses on the trunk can be considered in two dimensions. The direction of principal stress should coincide with
the longitudinal (L) and tangential (T) directions, with the
stress in the radial direction (R) being zero. Therefore, the longitudinal and transverse growth stresses (σL, σT) can be calculated as follows (Sasaki et al. 1978):
σ L = − EL ( ε L + VTL ε ) / (1 − VTL VLT )
T
(1)
and
σ L = − ET ( ε T + VLT ε ) / (1 − VTL VLT ),
L
(2)
where EL is the longitudinal modulus of elasticity, ET is the
transverse modulus of elasticity, εL is measured longitudinal
released strain, εT is measured transverse released strain, and
VLT and VTL are Poisson’s ratio. The true longitudinal strain (
ε ′L ) and true transverse residual strain (ε ′T ) can be calculated
as:
ε ′L = ( ε L + VTL ε ) / (1 − VTL VLT )
T
(3)
and
ε ′T = ( ε T + VLT ε ) / (1 − VTL VLT ).
L
(4)
Because VTL is very small, longitudinal growth stress can be
assumed to be an axial stress and can be simplified as:
σ L = − ε L EL .
(5)
In this experiment, only EL was measured, so only longitudinal
stresses that relate to the distortion of sawn timber and deformation during processing are discussed.
Results and discussion
Peripheral distribution of growth strain on leaning trunks
Large released strains were detected on the lower side (180°)
of the leaning trunk in both the longitudinal and transverse directions (Figure 3). The released longitudinal surface strains
were +3039 µε, +886 µε, and +2948 µε for Trees A, B and C,
respectively, with a mean of +2291 µε. A positive microstrain
value indicates an extension strain, implying that the lower
side suffers from compression stresses. Because the trees were
alive when measured, no modulus of elasticity or values for
true growth stress (Equation 5) could be obtained. Because
only tensile stress is normally found on erect trunks (Huang et
al. 1998), the compression stress on the lower side of the leaning trunks must have originated from the compression wood.
Boyd (1980) also detected a great extension strain (+1800 µε)
on the lower side of compression wood of Pinus radiata
Figure 3. Peripheral distribution of released surface strain in longitudinal (εL) and transverse directions (εT) in leaning trunks. The strain is
the mean of Trees A, B and C.
D. Don. Other locations on the peripheral trunk, in addition to
the lower side, showed small positive and negative released
strains. Thus, an erect trunk has a uniform circumferential distribution of released strains, whereas there are large variations
in leaning trunks.
The transverse growth strain showed negative values (contraction released strain) on the lower side (180°) and positive
values (extension released strain) at other locations (Figure 3).
Positive values indicate compression stress and negative values indicate tensile stress. This observation seems to conflict
with the theoretical compression stress of normal wood (Boyd
1972, Archer and Bynes 1974) and the measured values for
trees containing reaction wood (Okuyama et al. 1983).
Surface growth stress is a combination of longitudinal and
transverse stresses. The calculation of true transverse strain
needs to consider the effect of Poisson’s ratio and uses Equation 4. Longitudinal released strain (εL) of the lower side of a
leaning trunk (180°) equaled +2291 µε, and transverse released strain (εT) equaled –927 µε. Using the data from
Cryptomeria japonica (Sasaki et al. 1978), VLT = 0.46, VTL =
0.02, the true strains (ε ′L and ε ′T ), calculated using Equations 3
and 4, were +2294 and +128 µε, respectively. Because ε ′L and
εL are very close, it is possible to calculate longitudinal stress
with Equation 5. However, ε ′T and εT differ greatly in magnitude and also in sign. The value of εT indicates the existence of
tension stress, whereas the value of ε ′T indicates the existence
of compression stress. Thus, the measured transverse strain is
only an apparent value that suggests the existence of tensile
stress; however, after correcting with Poisson’s ratio, the existence of compression stress, as in normal wood, is indicated.
Therefore, we conclude that corrected transverse growth stress
should be calculated with Equation 2, and longitudinal stress
with Equation 5. All three standing trees showed a large
amount of released longitudinal extension strain on the lower
side of the leaning trunk, indicating a large amount of compression stress. This compression stress is entirely associated
with the specialized tissue of compression wood. Yamamoto
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HUANG, CHEN, LIN AND CHEN
et al. (1991) observed that the longitudinal compression
growth stresses in compression wood increase with increasing
microfibril angle of the S2 layer in the cell wall, and with the
lignin content of wood. This suggests that lignin swelling
takes part in the generation of compression stress in compression wood. Compression wood usually has a higher lignin content and greater microfibril angle than normal wood. The
magnitude of the compression stress can be used to evaluate
the extent of development of compression wood.
Influence of tree height on surface growth stress
The cross sections taken every 1–1.5 m from the leaning portion of the trunk of Tree E exhibited eccentric growth where
compression wood occurred (Figure 4). Great extension strain
(positive value) was detected on the lower side of the leaning
trunk within a distance of 5 m from the stump, indicating the
existence of compression stress (Figure 5a). Usually, only tension stress is found on the surface of erect trunks. The lateral
side below 3 m also showed extension strain; this is probably
because the large area of compression wood influenced the lateral side of the trunk. The upper side below 2 m showed slight
extension strain; this was probably caused by the effect of
spring back after cutting (Yamamoto et al. 1989) and by the release of resistant moment (see below). Theoretically, there
should be no extension strain, because there is no compression
wood on the upper side. Between 5 and 8 m from the stump,
the trunk showed a slight reflex upwards, the upper side
showed extension strain, and the lower side contraction strain.
Above 8 m from the stump, the erect normal trunk had no compression wood, so only contraction strain was observed on the
upper, lower and lateral sides.
Figure 4. Growth form and cross section at 1–1.5-m intervals along
the trunk of Tree E.
Figure 5. Effects of tree height on (a) released surface strain and (b)
released surface stress in the longitudinal direction of Tree E.
The relationship between surface growth stress and distance
from the stump was calculated with Equation 5 and is shown
in Figure 5b. Within 5 m of the stump, the compression stress
on the lower side of the leaning trunk apparently resulted from
compression wood that generates an expansive force inside
the trunk forcing trunk growth upward. Thus, compression
wood of conifers has developed specialized tissue in response
to changes in the environment.
With respect to surface transverse growth strain, the lower
side of the leaning trunk showed contraction strain, the other
sides showed extension strains (Figure 3). If we consider Poisson’s effect of longitudinal stress, the true transverse strain (
ε ′T , Equation 4) on the lower side of the leaning trunk becomes
extension strain, indicating that transverse stress is compression stress (not shown). Apparently both erect trunks and compression wood exhibit compression stress in the transverse
direction. From the physiological viewpoint, transverse compression stress could prevent longitudinal splitting of the trunk
as a result of damage by freezing temperatures, or from compression stress on the lower side of leaning trunks or branches.
Kubler (1987) studied the theoretical distribution of growth
stress in the trunk and predicted logarithmic relationships of
transverse stress in the radial direction. He concluded that
compression stress prevails on the outside of the trunk, and
tension stress on the inside. In order to reach mechanical equilibrium, radial stress should be equivalent to tensile stress,
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which is distributed increasingly from the outside to the inside
of the trunk and also exists in logarithmic relationships.
Distribution of residual stress within the trunk
Tree D showed curvature below breast height (Figure 2) and
almost no eccentric growth. At a height of 3.5 m, the distribution of internal strain (Figure 6a) is similar to that of normal
wood. Contraction strain or tension stress was found outside,
and extension strain or compression stress inside. The maximal residual strain near the peripheral surface was –958 µε,
and +1665 µε near the center. At 0.8-m height, complicated internal longitudinal residual strain was found in the leaning
trunk (Figure 6b), with variations between –2200 and
+1600 µε. The internal residual strain of the leaning trunk of
Tree F is shown in Figure 7a. Both upper and lower sides exhibited extension strain, but there was contraction strain inside. The contraction strain had a value of less than –7000 µε,
indicating increased tension. The distributions of residual
strain (Figure 7a) and internal stress (Figure 7b) in the leaning
trunk of Tree F are opposite to those of an erect trunk (Figure 6a). Compression stress was found outside with a value
about 10 MPa, and tension stress inside with a value reaching
25 MPa. Comparing Figures 6b and 7a, Tree D showed no apparent eccentric growth, whereas Tree F showed eccentric
growth. In other words, the pith of Tree F deviated from the
Figure 7. Distribution of (a) longitudinal released strain and (b) residual stress in the leaning trunk with eccentric growth (Tree F).
Figure 6. Distribution of (a) longitudinal released strain in the erect
and (b) leaning portions of the trunk without eccentric growth
(Tree D).
center in the elliptical cross section, whereas the pith of Tree D
was located in the center. Growth stress accumulates in the
trunk each year, and the distributions of stresses and growth
rings are closely related. Therefore, eccentric growth should
affect the distribution of residual stress. However, an elliptical
trunk, without eccentric growth, has a more complicated internal strain distribution (Figure 6b) than a trunk with eccentric
growth (Figure 7a). This might be associated with the action of
compression wood in the leaning trunk. Few studies have been
conducted on the distribution of internal stresses in leaning
trunks. Watanabe (1967) investigated the strain distribution in
a Chamecyparis obtusa Endl. tree containing compression
wood. The entire compression wood side was under compression stress, as was the outer part of the opposite side. The inner
portion of the opposite side, however, was under tension
stress. In contrast, we found that the inner portion of the compression side was under tension (Figure 7b). The mechanism
of reorientation of a leaning stem has been explained as the expansion of compression wood in the axial direction pushing
the trunk into the vertical position (Timell 1986b, Niklas 1992,
Mattheck and Kubler 1995). However, the mechanism by
which the compression wood expands along the grain of the
trunk has not yet been fully clarified. We speculate that compression stress exerted by the compression wood at the lower
side of a leaning trunk will introduce a resistant moment on the
cross section. The leaning trunk must bend upward to relieve
the internal moment and obtain a mechanical equilibrium.
During the bend upward, the lower side of the trunk generates
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HUANG, CHEN, LIN AND CHEN
tensile stress and the upper side generates compression stress.
These stresses are then superimposed on the original internal
growth stress. Thus, the measured internal stress distribution,
which is different from that in a normal trunk, is the sum of the
original residual stress and the bending stress. This stress distribution is further complicated by the accumulation of newly
generated growth stress each year. Additional studies with
new techniques are needed to elucidate the physiological significance of stress and strain in tree growth.
Acknowledgments
This research was supported financially by the National Science
Council, Taiwan (NSC87-2313-B-054-012). This paper is Contribution No. 162 of the Taiwan Forestry Research Institute.
References
Archer, R.R. 1986. Growth stresses and strains in trees. SpringerVerlag, New York, pp 203–204.
Archer, R.R. and F.E. Bynes. 1974. On the distribution of tree growth
stresses. Part l: An anisotropic plane strain theory. Wood Sci.
Technol. 8:184–196.
Archer, R.R. 1987. On the origin of growth stresses in trees. Wood
Sci. Technol. 21:139–154.
Boyd, J.D. 1972. Tree growth stresses. V. Evidence of an origin in differentiation and lignification. Wood Sci. Technol. 6:251–262.
Boyd, J.D. 1980. Relationship between fibre morphology, growth
strain and physical properties of wood. Aust. For. Res. 10:
337–360.
Huang, Y.S., S.S. Chen and Y.S. Chen. 1998. Study on growth stress
in trees. I. The growth stress distribution of planted Cryptomeria
japonica. Quart. J. Chin. For. 31:177–186. In Chinese.
Kubler, H. 1987. Growth stresses in trees and related wood properties. For. Abstr. 48:131–189.
Niklas, K.J. 1992. Plant biomechanics: an engineering approach to
plant form and function. Univ. Chicago Press, pp 420–423.
Mattheck, C. and H. Kubler. 1995. Wood—the internal optimization
of trees. Springer-Verlag, New York, pp 63–89.
Okuyama, T. and Y. Sasaki. 1979. Crooking during lumbering due to
residual stress in the tree. Mokuzai Gakkaishi 25:681–687.
Okuyama, T., A. Kawai, Y. Kikata and Y. Sasaki. 1983. Growth
stresses and uneven gravitational stimulus in trees containing reaction wood. Mokuzai Gakkaishi 29:190–196.
Okuyama, T., H. Yamamoto and Y. Murase. 1988. Quality improvement in small log of sugi by direct heating method. Mokuzai
Kogyo 43:359–363. In Japanese.
Panshin, A.J., C. deZeeuw and H.P. Brown. 1964. Textbook of wood
technology. McGraw-Hill Book Co., New York, pp 257–276.
Sasaki, Y., T. Okuyama and Y. Kikata. 1978. The evolution process
of the growth stress in the tree: the surface stress on the tree.
Mokuzai Gakkaishi 24:149–157.
Timell, T.E. 1986a. Compression wood in gymnosperms, Vol. 1.
Springer-Verlag, New York, pp 63–89.
Timell, T.E. 1986b. Compression wood in gymnosperms, Vol. 3.
Springer-Verlag, New York, pp 1757–1791, 1799–1824.
Watanabe, H. 1967. A study of the origin of longitudinal growth
stress in tree stems. Bull. Kyushu Univ. For. 41:169–176.
Yamamoto, H., T. Okuyama and M. Iguchi. 1989. Measurement of
growth stresses on the surface of a leaning stem. Mokuzai
Gakkaishi 35:595–601. In Japanese.
Yamamoto, H., T. Okuyama, M. Yoshida and K. Sugiyama. 1991.
Generation process of growth stresses in cell walls. Growth stress
in compression wood. Mokuzai Gakkaishi 37:94–100.
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